Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D4×Dic131 | C2 | semidirect |
| 3. C2×#16862208 | C2 | semidirect |
| 4. #22553214 | C2 | semidirect |
| 5. #22553189 | C2 | semidirect |
| 6. #22553188 | C2 | semidirect |
| 7. #22553177 | C2 | semidirect |
| 8. #22553158 | C2 | semidirect |
| 9. #390×C131 | C2 | semidirect |
| 14. #16862242 | C4 | semidirect |
| 33. C2×D524 | C2×C4 | semidirect |
| 36. C2×C22⋊D131 | C2×C4 | semidirect |
| 49. C4×Dic131 | C2×C4 | semidirect |
| 50. C4×Dic131 | D4 | semidirect |
| 54. C2×D4×C131 | C2×C4 | semidirect |
| 123. C131 | #2328 | semidirect |
| 129. #390 | D131 | semidirect |
| 164. C2×D4 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862242 | 2 |
| C2×D4×Dic131 | 2 |
| C2×#16862208 | 2 |
| #22553214 | 2 |
| #22553189 | 2 |
| #22553188 | 2 |
| #22553177 | 2 |
| #22553158 | 2 |
| #390×C131 | 2 |
| #2328 | 131 |